Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. The Howard methods also assume that the species composition of the harvests are equal to the species composition of released fish, which may not be true and is evident in the logbook data. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds that when not met, values are borrowed from nearby areas Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is no uncertainty generated from uncertainty in the assmptions made such as species composition of the releases or when borrowing values from one area to another. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.
Time series 1999 - present 1977 - present

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was explored that loosened the assumption that logbook releases were a census. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Priors.

Priors range from uninformative to very informative or fixed. These will be covered once a satisfactorilly convergerd model is achieved.

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behavior and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 8.**- DSR rockfish (including yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 10.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 12.**- Residuals from logbook harvests

Figure 12.- Residuals from logbook harvests


SWHS residuals

**Figure 13.**- Residuals from SWHS harvests.

Figure 13.- Residuals from SWHS harvests.



**Figure 14.**- Residual of SWHS releases

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 15.**- Mean percent of harvest by charter anglers.

Figure 15.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 16.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 18.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 19.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 20.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 23.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 24.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 25.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 26.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 27.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 28.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 30.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 31.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_black 1 3.597051
beta0_yellow 4 2.118409
beta1_yellow 7 2.088668
beta2_yellow 2 2.014862
beta3_black 1 1.978517
beta0_black 1 1.645806
sd_comp 1 1.472437
beta3_yellow 6 1.459913
mu_beta0_yellow 1 1.358601
beta2_black 1 1.314766
parameter n badRhat_avg
tau_beta0_yellow 2 1.310779
beta0_pH 5 1.295521
beta1_pH 6 1.280327
beta1_pelagic 4 1.232110
beta2_pH 9 1.218223
beta0_pelagic 3 1.211077
beta2_pelagic 2 1.172752
tau_beta0_pH 1 1.153488
beta3_pH 1 1.123351
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta0_pelagic 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0
beta0_pH 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1
beta0_yellow 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0
beta1_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta1_pelagic 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0
beta1_pH 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1
beta1_yellow 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1
beta2_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta2_pelagic 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0
beta2_pH 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1
beta2_yellow 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
beta3_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
beta3_yellow 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1
mu_beta0_yellow 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.125 0.074 -0.260 -0.131 0.035
mu_bc_H[2] -0.096 0.046 -0.173 -0.101 0.010
mu_bc_H[3] -0.435 0.070 -0.568 -0.437 -0.292
mu_bc_H[4] -0.986 0.193 -1.385 -0.984 -0.624
mu_bc_H[5] 0.964 0.928 -0.153 0.786 3.328
mu_bc_H[6] -2.158 0.323 -2.788 -2.162 -1.515
mu_bc_H[7] -0.449 0.109 -0.669 -0.450 -0.238
mu_bc_H[8] 0.247 0.361 -0.369 0.214 1.044
mu_bc_H[9] -0.291 0.138 -0.567 -0.291 -0.022
mu_bc_H[10] -0.106 0.071 -0.237 -0.109 0.039
mu_bc_H[11] -0.124 0.038 -0.200 -0.124 -0.047
mu_bc_H[12] -0.253 0.107 -0.476 -0.252 -0.047
mu_bc_H[13] -0.132 0.078 -0.284 -0.133 0.025
mu_bc_H[14] -0.298 0.098 -0.496 -0.298 -0.111
mu_bc_H[15] -0.342 0.051 -0.444 -0.343 -0.243
mu_bc_H[16] -0.278 0.373 -0.934 -0.305 0.525
mu_bc_R[1] 1.353 0.151 1.062 1.355 1.654
mu_bc_R[2] 1.452 0.092 1.271 1.452 1.628
mu_bc_R[3] 1.399 0.142 1.118 1.397 1.675
mu_bc_R[4] 0.898 0.204 0.469 0.908 1.277
mu_bc_R[5] 1.152 0.476 0.188 1.160 2.092
mu_bc_R[6] -1.587 0.420 -2.420 -1.581 -0.766
mu_bc_R[7] 0.319 0.192 -0.053 0.312 0.682
mu_bc_R[8] 0.550 0.194 0.153 0.558 0.913
mu_bc_R[9] 0.331 0.207 -0.111 0.342 0.700
mu_bc_R[10] 1.291 0.138 1.021 1.297 1.551
mu_bc_R[11] 1.037 0.099 0.839 1.039 1.230
mu_bc_R[12] 0.816 0.201 0.413 0.815 1.208
mu_bc_R[13] 1.026 0.102 0.824 1.027 1.229
mu_bc_R[14] 0.890 0.142 0.611 0.889 1.159
mu_bc_R[15] 0.784 0.108 0.568 0.786 0.991
mu_bc_R[16] 1.094 0.127 0.841 1.094 1.339
tau_pH[1] 5.206 0.432 4.417 5.198 6.092
tau_pH[2] 2.054 0.222 1.634 2.047 2.520
tau_pH[3] 2.269 0.223 1.836 2.261 2.731
beta0_pH[1,1] 0.561 0.180 0.195 0.561 0.898
beta0_pH[2,1] 1.363 0.184 0.988 1.364 1.701
beta0_pH[3,1] 1.414 0.204 0.974 1.425 1.770
beta0_pH[4,1] 1.552 0.231 1.033 1.569 1.939
beta0_pH[5,1] -0.866 0.293 -1.487 -0.845 -0.366
beta0_pH[6,1] -0.667 0.441 -1.709 -0.598 -0.030
beta0_pH[7,1] -0.545 0.506 -1.809 -0.492 0.343
beta0_pH[8,1] -0.664 0.279 -1.295 -0.627 -0.218
beta0_pH[9,1] -0.661 0.293 -1.310 -0.641 -0.164
beta0_pH[10,1] 0.226 0.205 -0.193 0.236 0.603
beta0_pH[11,1] -0.092 0.171 -0.433 -0.086 0.222
beta0_pH[12,1] 0.475 0.183 0.113 0.477 0.824
beta0_pH[13,1] 0.008 0.146 -0.285 0.007 0.290
beta0_pH[14,1] -0.317 0.166 -0.643 -0.315 0.006
beta0_pH[15,1] -0.037 0.175 -0.394 -0.036 0.298
beta0_pH[16,1] -0.436 0.318 -1.220 -0.391 0.064
beta0_pH[1,2] 2.808 0.167 2.452 2.815 3.122
beta0_pH[2,2] 2.874 0.133 2.604 2.877 3.132
beta0_pH[3,2] 3.122 0.174 2.802 3.124 3.450
beta0_pH[4,2] 2.946 0.133 2.686 2.946 3.204
beta0_pH[5,2] 4.772 1.431 2.963 4.467 8.563
beta0_pH[6,2] 3.113 0.205 2.713 3.114 3.522
beta0_pH[7,2] 1.962 0.172 1.633 1.963 2.307
beta0_pH[8,2] 2.872 0.174 2.526 2.876 3.215
beta0_pH[9,2] 3.435 0.224 3.001 3.430 3.879
beta0_pH[10,2] 3.740 0.199 3.352 3.737 4.131
beta0_pH[11,2] -4.830 0.300 -5.438 -4.830 -4.259
beta0_pH[12,2] -4.767 0.388 -5.553 -4.755 -4.032
beta0_pH[13,2] -4.563 0.397 -5.333 -4.578 -3.760
beta0_pH[14,2] -5.612 0.485 -6.589 -5.594 -4.705
beta0_pH[15,2] -4.270 0.348 -4.928 -4.277 -3.587
beta0_pH[16,2] -4.868 0.389 -5.667 -4.863 -4.103
beta0_pH[1,3] 0.432 0.673 -1.116 0.497 1.465
beta0_pH[2,3] 2.198 0.155 1.900 2.197 2.491
beta0_pH[3,3] 2.517 0.142 2.239 2.516 2.803
beta0_pH[4,3] 2.963 0.156 2.659 2.964 3.257
beta0_pH[5,3] 2.183 2.039 -0.820 1.912 6.929
beta0_pH[6,3] -0.238 1.074 -2.053 -0.425 1.630
beta0_pH[7,3] -2.014 0.614 -3.374 -1.939 -1.021
beta0_pH[8,3] 0.292 0.192 -0.091 0.296 0.663
beta0_pH[9,3] -0.940 0.914 -3.638 -0.661 -0.022
beta0_pH[10,3] 0.265 0.803 -2.067 0.499 1.185
beta0_pH[11,3] -0.169 0.327 -0.801 -0.174 0.484
beta0_pH[12,3] -0.908 0.352 -1.659 -0.880 -0.294
beta0_pH[13,3] -0.140 0.314 -0.750 -0.143 0.462
beta0_pH[14,3] -0.286 0.260 -0.803 -0.291 0.228
beta0_pH[15,3] -0.745 0.292 -1.335 -0.739 -0.206
beta0_pH[16,3] -0.410 0.293 -0.994 -0.400 0.155
beta1_pH[1,1] 3.048 0.325 2.463 3.031 3.774
beta1_pH[2,1] 2.167 0.282 1.675 2.153 2.785
beta1_pH[3,1] 1.992 0.322 1.454 1.964 2.697
beta1_pH[4,1] 2.429 0.416 1.849 2.367 3.347
beta1_pH[5,1] 2.305 0.365 1.705 2.265 3.140
beta1_pH[6,1] 3.820 1.065 2.386 3.623 6.303
beta1_pH[7,1] 2.788 1.005 1.023 2.674 5.302
beta1_pH[8,1] 4.010 0.986 2.666 3.802 6.458
beta1_pH[9,1] 2.362 0.412 1.715 2.318 3.301
beta1_pH[10,1] 2.404 0.283 1.880 2.397 3.010
beta1_pH[11,1] 3.267 0.213 2.877 3.260 3.693
beta1_pH[12,1] 2.562 0.211 2.144 2.560 2.984
beta1_pH[13,1] 2.965 0.216 2.564 2.961 3.399
beta1_pH[14,1] 3.424 0.218 3.014 3.419 3.869
beta1_pH[15,1] 2.543 0.222 2.124 2.540 2.990
beta1_pH[16,1] 4.053 0.598 3.197 3.942 5.569
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.020 0.146 0.000 0.000 0.013
beta1_pH[4,2] 0.002 0.037 0.000 0.000 0.002
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.665 0.327 6.041 6.656 7.309
beta1_pH[12,2] 6.426 0.446 5.591 6.412 7.351
beta1_pH[13,2] 6.940 0.439 6.083 6.940 7.828
beta1_pH[14,2] 7.251 0.507 6.328 7.224 8.244
beta1_pH[15,2] 6.749 0.377 6.016 6.750 7.461
beta1_pH[16,2] 7.465 0.437 6.599 7.454 8.345
beta1_pH[1,3] 3.354 1.521 1.357 3.070 7.282
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 2.339 3.720 0.001 2.435 5.990
beta1_pH[6,3] 2.031 1.211 0.001 2.222 3.922
beta1_pH[7,3] 2.861 0.623 1.871 2.794 4.302
beta1_pH[8,3] 2.742 0.352 2.044 2.748 3.430
beta1_pH[9,3] 3.007 0.943 1.976 2.751 5.702
beta1_pH[10,3] 3.113 0.880 2.074 2.871 5.566
beta1_pH[11,3] 2.764 0.390 2.027 2.762 3.582
beta1_pH[12,3] 4.182 0.428 3.408 4.165 5.055
beta1_pH[13,3] 1.724 0.338 1.071 1.725 2.416
beta1_pH[14,3] 2.543 0.335 1.890 2.546 3.192
beta1_pH[15,3] 2.034 0.313 1.434 2.030 2.649
beta1_pH[16,3] 1.821 0.321 1.193 1.814 2.451
beta2_pH[1,1] 0.481 0.125 0.286 0.466 0.782
beta2_pH[2,1] 0.581 0.375 0.250 0.516 1.371
beta2_pH[3,1] 0.643 0.393 0.226 0.553 1.684
beta2_pH[4,1] 0.463 0.182 0.190 0.441 0.864
beta2_pH[5,1] 1.410 0.995 0.227 1.247 3.886
beta2_pH[6,1] 0.187 0.063 0.096 0.176 0.338
beta2_pH[7,1] 0.009 0.054 0.000 0.000 0.057
beta2_pH[8,1] 0.243 0.088 0.129 0.229 0.448
beta2_pH[9,1] 0.416 0.189 0.162 0.383 0.857
beta2_pH[10,1] 0.608 0.278 0.288 0.548 1.284
beta2_pH[11,1] 0.781 0.210 0.472 0.751 1.261
beta2_pH[12,1] 1.334 0.479 0.732 1.234 2.574
beta2_pH[13,1] 0.737 0.216 0.415 0.701 1.251
beta2_pH[14,1] 0.839 0.214 0.535 0.805 1.330
beta2_pH[15,1] 0.805 0.291 0.421 0.746 1.558
beta2_pH[16,1] 0.383 0.163 0.176 0.341 0.811
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -0.743 3.862 -8.411 -0.681 6.728
beta2_pH[4,2] -0.763 3.958 -8.556 -0.775 6.793
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -8.642 3.175 -16.187 -8.023 -4.049
beta2_pH[12,2] -7.131 3.884 -15.604 -6.788 -0.996
beta2_pH[13,2] -6.897 3.732 -15.499 -6.362 -1.634
beta2_pH[14,2] -7.571 3.512 -15.553 -7.020 -2.372
beta2_pH[15,2] -8.478 2.682 -14.545 -7.941 -4.509
beta2_pH[16,2] -8.619 3.224 -16.233 -8.130 -4.000
beta2_pH[1,3] 14.174 120.056 0.079 0.288 100.614
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.050 6.277 -0.588 6.918 22.500
beta2_pH[6,3] 8.029 6.166 -0.059 6.982 22.752
beta2_pH[7,3] 7.957 6.069 0.647 6.640 22.154
beta2_pH[8,3] 9.115 5.658 1.436 7.955 22.643
beta2_pH[9,3] 7.551 6.402 0.300 6.311 22.611
beta2_pH[10,3] 7.193 6.484 0.336 5.985 22.878
beta2_pH[11,3] -2.063 1.853 -7.522 -1.569 -0.577
beta2_pH[12,3] -2.090 1.647 -6.885 -1.666 -0.923
beta2_pH[13,3] -2.665 2.234 -9.008 -1.992 -0.709
beta2_pH[14,3] -2.587 1.996 -8.872 -1.977 -0.902
beta2_pH[15,3] -2.788 2.171 -8.763 -2.083 -0.974
beta2_pH[16,3] -2.784 2.216 -8.964 -2.081 -0.902
beta3_pH[1,1] 35.898 0.829 34.337 35.878 37.613
beta3_pH[2,1] 33.591 1.189 31.519 33.520 36.327
beta3_pH[3,1] 33.600 1.057 31.659 33.583 35.824
beta3_pH[4,1] 33.891 1.347 31.705 33.806 36.620
beta3_pH[5,1] 27.784 1.183 26.442 27.502 31.192
beta3_pH[6,1] 38.581 3.125 32.834 38.475 44.781
beta3_pH[7,1] 30.721 8.039 18.483 30.245 45.041
beta3_pH[8,1] 39.935 2.157 36.284 39.654 44.815
beta3_pH[9,1] 30.715 1.538 28.104 30.599 33.962
beta3_pH[10,1] 32.697 0.900 30.989 32.665 34.539
beta3_pH[11,1] 30.306 0.477 29.382 30.303 31.279
beta3_pH[12,1] 30.155 0.404 29.362 30.156 30.925
beta3_pH[13,1] 33.181 0.591 32.052 33.174 34.360
beta3_pH[14,1] 32.017 0.453 31.162 31.999 32.948
beta3_pH[15,1] 31.172 0.615 29.943 31.163 32.372
beta3_pH[16,1] 32.077 1.034 30.458 31.929 34.542
beta3_pH[1,2] 30.146 7.895 18.472 29.385 44.819
beta3_pH[2,2] 30.099 7.968 18.501 29.176 44.923
beta3_pH[3,2] 30.022 8.128 18.432 28.819 45.204
beta3_pH[4,2] 29.951 7.855 18.494 29.064 44.792
beta3_pH[5,2] 30.200 8.043 18.472 29.481 45.018
beta3_pH[6,2] 29.870 7.913 18.467 28.793 44.887
beta3_pH[7,2] 29.959 7.872 18.477 29.025 44.860
beta3_pH[8,2] 29.866 7.978 18.541 28.803 44.977
beta3_pH[9,2] 29.988 7.970 18.590 28.873 44.964
beta3_pH[10,2] 29.865 7.907 18.535 28.910 44.948
beta3_pH[11,2] 43.404 0.175 43.126 43.386 43.762
beta3_pH[12,2] 43.187 0.185 42.918 43.149 43.684
beta3_pH[13,2] 43.860 0.143 43.466 43.898 44.038
beta3_pH[14,2] 43.313 0.202 43.060 43.258 43.794
beta3_pH[15,2] 43.408 0.189 43.117 43.381 43.791
beta3_pH[16,2] 43.501 0.181 43.177 43.498 43.833
beta3_pH[1,3] 38.972 2.964 33.613 39.181 45.011
beta3_pH[2,3] 30.500 8.153 18.526 29.781 45.038
beta3_pH[3,3] 30.307 7.949 18.495 29.682 44.898
beta3_pH[4,3] 30.448 7.980 18.595 29.627 44.900
beta3_pH[5,3] 27.701 7.298 18.296 26.008 44.185
beta3_pH[6,3] 28.048 6.493 18.800 25.912 44.151
beta3_pH[7,3] 26.661 0.970 25.041 26.509 28.980
beta3_pH[8,3] 41.483 0.260 41.053 41.479 41.946
beta3_pH[9,3] 32.769 1.800 27.418 33.422 34.194
beta3_pH[10,3] 35.475 1.262 32.036 35.963 36.829
beta3_pH[11,3] 41.784 0.780 40.214 41.829 43.232
beta3_pH[12,3] 41.732 0.392 40.971 41.746 42.516
beta3_pH[13,3] 42.790 0.904 41.102 42.783 44.937
beta3_pH[14,3] 41.089 0.553 39.955 41.110 42.138
beta3_pH[15,3] 42.659 0.624 41.316 42.728 43.711
beta3_pH[16,3] 42.915 0.708 41.330 43.013 44.149
beta0_pelagic[1] 2.217 0.129 1.973 2.213 2.474
beta0_pelagic[2] 1.520 0.123 1.280 1.522 1.758
beta0_pelagic[3] -0.319 1.005 -3.175 -0.104 0.883
beta0_pelagic[4] -0.134 0.982 -2.506 0.105 1.133
beta0_pelagic[5] 1.170 0.248 0.660 1.170 1.650
beta0_pelagic[6] 1.466 0.274 0.871 1.481 1.974
beta0_pelagic[7] 1.661 0.223 1.275 1.642 2.161
beta0_pelagic[8] 1.759 0.208 1.353 1.748 2.226
beta0_pelagic[9] 2.508 0.321 1.871 2.523 3.094
beta0_pelagic[10] 2.535 0.198 2.119 2.539 2.913
beta0_pelagic[11] 0.082 0.569 -1.574 0.255 0.726
beta0_pelagic[12] 1.682 0.145 1.394 1.685 1.962
beta0_pelagic[13] 0.320 0.195 -0.123 0.335 0.667
beta0_pelagic[14] -0.120 0.312 -0.827 -0.086 0.376
beta0_pelagic[15] -0.256 0.134 -0.529 -0.258 0.001
beta0_pelagic[16] 0.291 0.292 -0.519 0.365 0.672
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.854 1.728 0.000 1.551 7.340
beta1_pelagic[4] 1.495 1.304 0.000 1.143 4.655
beta1_pelagic[5] -0.063 0.312 -0.670 -0.061 0.544
beta1_pelagic[6] -0.101 0.450 -0.861 -0.162 0.745
beta1_pelagic[7] -0.012 0.330 -0.647 -0.019 0.642
beta1_pelagic[8] 0.002 0.291 -0.554 0.000 0.609
beta1_pelagic[9] 0.190 0.485 -0.760 0.287 0.947
beta1_pelagic[10] 0.061 0.263 -0.444 0.061 0.584
beta1_pelagic[11] 3.504 1.257 2.066 3.123 6.852
beta1_pelagic[12] 2.802 0.294 2.237 2.793 3.419
beta1_pelagic[13] 2.919 0.738 1.761 2.845 4.561
beta1_pelagic[14] 4.341 1.069 2.809 4.133 6.979
beta1_pelagic[15] 2.928 0.260 2.420 2.928 3.442
beta1_pelagic[16] 3.599 0.969 2.668 3.279 6.516
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.517 2.075 0.000 0.106 4.403
beta2_pelagic[4] 0.994 2.769 0.000 0.341 2.729
beta2_pelagic[5] -0.001 0.661 -1.395 -0.013 1.412
beta2_pelagic[6] -0.114 0.695 -1.489 -0.157 1.370
beta2_pelagic[7] 0.000 0.693 -1.453 0.009 1.423
beta2_pelagic[8] -0.010 0.656 -1.479 -0.007 1.340
beta2_pelagic[9] 0.172 0.698 -1.315 0.229 1.564
beta2_pelagic[10] -0.015 0.655 -1.458 0.012 1.342
beta2_pelagic[11] 2.540 4.776 0.096 0.338 15.740
beta2_pelagic[12] 6.823 5.571 1.244 5.062 22.258
beta2_pelagic[13] 0.988 2.060 0.195 0.468 6.344
beta2_pelagic[14] 0.319 0.147 0.154 0.287 0.688
beta2_pelagic[15] 6.899 5.177 1.446 5.404 20.806
beta2_pelagic[16] 5.466 5.787 0.178 4.047 21.554
beta3_pelagic[1] 30.098 8.003 18.417 29.158 44.907
beta3_pelagic[2] 29.811 7.999 18.404 28.567 44.929
beta3_pelagic[3] 29.698 6.849 18.646 29.142 44.275
beta3_pelagic[4] 25.714 5.720 18.485 24.766 42.235
beta3_pelagic[5] 30.321 8.274 18.523 29.128 45.342
beta3_pelagic[6] 32.002 6.683 18.909 31.942 44.123
beta3_pelagic[7] 29.407 7.425 18.465 28.549 44.542
beta3_pelagic[8] 29.551 7.959 18.418 28.099 44.769
beta3_pelagic[9] 30.658 6.252 18.989 30.635 42.957
beta3_pelagic[10] 29.645 8.088 18.419 28.260 44.825
beta3_pelagic[11] 42.190 2.020 37.200 42.961 45.205
beta3_pelagic[12] 43.456 0.257 43.020 43.452 43.935
beta3_pelagic[13] 42.909 1.294 40.500 42.852 45.590
beta3_pelagic[14] 42.281 1.719 38.829 42.285 45.592
beta3_pelagic[15] 43.204 0.244 42.680 43.187 43.699
beta3_pelagic[16] 43.173 0.742 41.434 43.223 44.986
mu_beta0_pelagic[1] 0.769 1.061 -1.702 0.895 2.610
mu_beta0_pelagic[2] 1.823 0.396 0.997 1.837 2.579
mu_beta0_pelagic[3] 0.329 0.486 -0.706 0.344 1.288
tau_beta0_pelagic[1] 0.703 1.067 0.051 0.361 3.415
tau_beta0_pelagic[2] 2.684 2.888 0.256 1.971 9.380
tau_beta0_pelagic[3] 1.540 1.167 0.180 1.260 4.587
beta0_yellow[1] -0.518 0.176 -0.892 -0.507 -0.198
beta0_yellow[2] 0.506 0.190 0.158 0.519 0.812
beta0_yellow[3] -0.298 0.194 -0.691 -0.289 0.047
beta0_yellow[4] 0.845 0.271 0.107 0.889 1.214
beta0_yellow[5] -0.982 0.610 -2.040 -1.045 0.203
beta0_yellow[6] 0.237 0.765 -1.253 0.112 1.366
beta0_yellow[7] 1.053 0.161 0.747 1.053 1.360
beta0_yellow[8] 0.973 0.250 0.475 0.998 1.298
beta0_yellow[9] 0.003 0.873 -2.099 0.419 0.928
beta0_yellow[10] 0.380 0.216 -0.011 0.371 0.791
beta0_yellow[11] -1.969 0.465 -2.874 -1.975 -1.038
beta0_yellow[12] -3.649 0.416 -4.495 -3.634 -2.878
beta0_yellow[13] -3.702 0.464 -4.691 -3.665 -2.889
beta0_yellow[14] -2.156 0.512 -3.108 -2.176 -1.113
beta0_yellow[15] -2.851 0.420 -3.780 -2.826 -2.083
beta0_yellow[16] -2.397 0.434 -3.242 -2.400 -1.559
beta1_yellow[1] 0.625 1.010 0.000 0.475 2.160
beta1_yellow[2] 1.052 0.374 0.564 1.003 1.940
beta1_yellow[3] 0.666 0.336 0.067 0.658 1.175
beta1_yellow[4] 1.345 0.740 0.622 1.161 3.795
beta1_yellow[5] 2.292 3.177 0.000 2.510 5.269
beta1_yellow[6] 2.646 2.086 0.000 3.244 6.129
beta1_yellow[7] 3.802 4.583 0.000 3.207 15.904
beta1_yellow[8] 2.050 4.977 0.000 0.637 9.527
beta1_yellow[9] 2.221 3.095 0.000 2.109 7.903
beta1_yellow[10] 1.356 1.199 0.000 1.626 3.430
beta1_yellow[11] 2.118 0.455 1.228 2.113 3.003
beta1_yellow[12] 2.447 0.423 1.665 2.432 3.342
beta1_yellow[13] 2.813 0.462 2.003 2.784 3.790
beta1_yellow[14] 2.217 0.508 1.165 2.223 3.177
beta1_yellow[15] 2.095 0.420 1.319 2.074 3.000
beta1_yellow[16] 2.155 0.438 1.295 2.158 2.993
beta2_yellow[1] -4.641 3.430 -12.217 -4.031 -0.092
beta2_yellow[2] -4.633 3.443 -12.659 -4.012 -0.187
beta2_yellow[3] -4.505 3.452 -12.446 -3.864 -0.169
beta2_yellow[4] -4.094 3.593 -12.112 -3.351 -0.095
beta2_yellow[5] -4.671 3.247 -12.229 -4.081 -0.384
beta2_yellow[6] -1.712 3.356 -10.640 0.177 0.247
beta2_yellow[7] -4.878 3.152 -12.451 -4.328 -0.261
beta2_yellow[8] -4.184 3.296 -11.945 -3.510 -0.030
beta2_yellow[9] -2.662 3.667 -11.460 -0.435 0.243
beta2_yellow[10] -4.780 3.148 -12.138 -4.180 -0.432
beta2_yellow[11] -5.418 3.082 -12.497 -4.833 -1.199
beta2_yellow[12] -5.717 2.951 -12.596 -5.202 -1.556
beta2_yellow[13] -5.575 2.891 -12.248 -4.981 -1.652
beta2_yellow[14] -5.718 3.092 -13.090 -5.289 -1.092
beta2_yellow[15] -5.113 3.011 -11.874 -4.509 -1.065
beta2_yellow[16] -5.627 2.908 -12.274 -5.151 -1.425
beta3_yellow[1] 26.478 7.277 18.330 23.428 44.172
beta3_yellow[2] 29.123 1.837 26.190 28.857 32.839
beta3_yellow[3] 33.008 3.020 25.985 32.930 39.659
beta3_yellow[4] 28.951 3.347 21.838 27.939 35.861
beta3_yellow[5] 32.297 4.966 19.500 33.183 43.221
beta3_yellow[6] 37.775 7.685 19.499 40.833 45.739
beta3_yellow[7] 24.079 7.295 18.406 20.328 43.861
beta3_yellow[8] 27.304 7.066 18.390 25.647 44.324
beta3_yellow[9] 32.892 9.009 18.400 34.703 45.495
beta3_yellow[10] 29.754 5.041 19.139 29.405 43.409
beta3_yellow[11] 45.286 0.809 44.087 45.414 45.975
beta3_yellow[12] 43.307 0.371 42.564 43.280 44.006
beta3_yellow[13] 44.871 0.401 43.971 44.962 45.535
beta3_yellow[14] 44.270 0.811 43.119 44.256 45.784
beta3_yellow[15] 45.152 0.524 44.185 45.115 45.971
beta3_yellow[16] 44.513 0.714 43.377 44.510 45.789
mu_beta0_yellow[1] 0.113 0.532 -0.960 0.116 1.174
mu_beta0_yellow[2] 0.263 0.569 -1.049 0.325 1.238
mu_beta0_yellow[3] -2.456 0.613 -3.419 -2.547 -0.939
tau_beta0_yellow[1] 1.925 3.310 0.088 1.221 7.301
tau_beta0_yellow[2] 1.684 2.192 0.132 1.028 7.511
tau_beta0_yellow[3] 1.496 1.951 0.110 0.958 6.055
beta0_black[1] 0.001 0.194 -0.353 -0.002 0.380
beta0_black[2] 1.917 0.129 1.665 1.914 2.168
beta0_black[3] 1.315 0.133 1.056 1.315 1.571
beta0_black[4] 2.429 0.131 2.170 2.431 2.688
beta0_black[5] 1.588 1.948 -2.421 1.613 5.731
beta0_black[6] 1.655 1.965 -2.796 1.695 5.639
beta0_black[7] 1.620 1.956 -2.691 1.679 5.554
beta0_black[8] 1.292 0.223 0.860 1.292 1.731
beta0_black[9] 2.447 0.250 1.949 2.448 2.940
beta0_black[10] 1.473 0.133 1.212 1.473 1.725
beta0_black[11] 3.486 0.152 3.174 3.486 3.779
beta0_black[12] 4.860 0.173 4.519 4.864 5.203
beta0_black[13] -0.109 0.231 -0.569 -0.107 0.336
beta0_black[14] 2.858 0.152 2.561 2.861 3.160
beta0_black[15] 1.294 0.151 1.004 1.294 1.593
beta0_black[16] 4.274 0.162 3.960 4.274 4.603
beta2_black[1] 2.434 3.044 -4.102 2.324 8.659
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.151 1.704 -6.963 -1.565 -0.457
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 38.257 6.873 19.787 41.461 43.629
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.250 0.730 37.541 39.304 40.537
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.268 0.196 -0.646 -0.271 0.129
beta4_black[2] 0.235 0.184 -0.114 0.233 0.607
beta4_black[3] -0.935 0.192 -1.310 -0.938 -0.557
beta4_black[4] 0.419 0.216 -0.005 0.419 0.849
beta4_black[5] 0.228 2.601 -4.671 0.149 5.369
beta4_black[6] 0.275 2.460 -4.306 0.182 5.567
beta4_black[7] 0.312 2.650 -4.329 0.188 5.312
beta4_black[8] -0.698 0.380 -1.456 -0.691 0.024
beta4_black[9] 1.468 1.005 -0.131 1.345 3.769
beta4_black[10] 0.027 0.189 -0.332 0.027 0.395
beta4_black[11] -0.697 0.215 -1.113 -0.696 -0.265
beta4_black[12] 0.167 0.317 -0.433 0.158 0.819
beta4_black[13] -1.178 0.221 -1.620 -1.179 -0.745
beta4_black[14] -0.184 0.227 -0.615 -0.192 0.260
beta4_black[15] -0.891 0.205 -1.300 -0.892 -0.505
beta4_black[16] -0.600 0.227 -1.040 -0.597 -0.146
mu_beta0_black[1] 1.289 0.916 -0.769 1.354 3.016
mu_beta0_black[2] 1.611 0.929 -0.549 1.663 3.442
mu_beta0_black[3] 2.541 0.961 0.434 2.564 4.407
tau_beta0_black[1] 0.680 0.632 0.060 0.488 2.324
tau_beta0_black[2] 1.879 3.312 0.055 0.828 10.584
tau_beta0_black[3] 0.240 0.158 0.052 0.203 0.654
beta0_dsr[11] -2.904 0.288 -3.455 -2.901 -2.348
beta0_dsr[12] 4.535 0.389 3.995 4.540 5.088
beta0_dsr[13] -1.368 0.344 -2.002 -1.352 -0.768
beta0_dsr[14] -3.648 0.511 -4.643 -3.654 -2.655
beta0_dsr[15] -1.931 0.283 -2.489 -1.924 -1.382
beta0_dsr[16] -2.979 0.368 -3.696 -2.982 -2.251
beta1_dsr[11] 4.835 0.302 4.270 4.832 5.424
beta1_dsr[12] 6.560 9.096 2.188 5.016 19.371
beta1_dsr[13] 2.884 0.409 2.286 2.856 3.608
beta1_dsr[14] 6.315 0.542 5.279 6.303 7.375
beta1_dsr[15] 3.331 0.284 2.784 3.326 3.909
beta1_dsr[16] 5.801 0.384 5.036 5.802 6.566
beta2_dsr[11] -8.299 2.379 -14.069 -7.981 -4.672
beta2_dsr[12] -7.056 2.699 -12.966 -6.869 -2.186
beta2_dsr[13] -6.447 2.774 -12.342 -6.365 -1.278
beta2_dsr[14] -6.059 2.663 -11.835 -5.918 -1.730
beta2_dsr[15] -7.755 2.371 -13.221 -7.471 -3.811
beta2_dsr[16] -7.978 2.381 -13.549 -7.687 -4.224
beta3_dsr[11] 43.490 0.150 43.205 43.487 43.777
beta3_dsr[12] 33.997 0.761 32.251 34.129 34.807
beta3_dsr[13] 43.251 0.340 42.799 43.193 43.869
beta3_dsr[14] 43.357 0.242 43.081 43.285 43.972
beta3_dsr[15] 43.510 0.184 43.174 43.514 43.848
beta3_dsr[16] 43.440 0.157 43.174 43.426 43.769
beta4_dsr[11] 0.582 0.217 0.157 0.577 1.024
beta4_dsr[12] 0.234 0.438 -0.633 0.241 1.147
beta4_dsr[13] -0.164 0.218 -0.599 -0.161 0.252
beta4_dsr[14] 0.148 0.251 -0.351 0.150 0.648
beta4_dsr[15] 0.720 0.212 0.311 0.720 1.132
beta4_dsr[16] 0.139 0.229 -0.312 0.141 0.584
beta0_slope[11] -1.947 0.164 -2.267 -1.951 -1.621
beta0_slope[12] -4.681 0.267 -5.212 -4.675 -4.166
beta0_slope[13] -1.328 0.204 -1.735 -1.319 -0.974
beta0_slope[14] -2.643 0.178 -2.989 -2.643 -2.290
beta0_slope[15] -1.367 0.167 -1.682 -1.370 -1.042
beta0_slope[16] -2.721 0.171 -3.061 -2.721 -2.396
beta1_slope[11] 4.605 0.301 4.014 4.601 5.185
beta1_slope[12] 5.018 0.520 4.023 5.007 6.051
beta1_slope[13] 2.884 0.472 2.212 2.840 3.972
beta1_slope[14] 6.542 0.553 5.487 6.539 7.649
beta1_slope[15] 3.048 0.284 2.507 3.036 3.613
beta1_slope[16] 5.381 0.404 4.597 5.381 6.154
beta2_slope[11] 8.011 2.382 4.316 7.671 13.533
beta2_slope[12] 7.181 2.513 2.800 6.897 13.037
beta2_slope[13] 5.803 2.886 0.492 5.867 11.643
beta2_slope[14] 6.555 2.448 2.508 6.300 12.163
beta2_slope[15] 7.534 2.426 3.758 7.239 13.213
beta2_slope[16] 7.627 2.353 3.888 7.348 13.321
beta3_slope[11] 43.469 0.154 43.190 43.462 43.765
beta3_slope[12] 43.409 0.228 43.076 43.379 43.873
beta3_slope[13] 43.622 0.434 42.915 43.687 44.290
beta3_slope[14] 43.318 0.174 43.091 43.275 43.753
beta3_slope[15] 43.516 0.193 43.164 43.518 43.873
beta3_slope[16] 43.457 0.170 43.174 43.445 43.806
beta4_slope[11] -0.566 0.219 -0.996 -0.565 -0.152
beta4_slope[12] -1.374 0.649 -2.856 -1.303 -0.307
beta4_slope[13] 0.049 0.223 -0.378 0.048 0.497
beta4_slope[14] -0.182 0.258 -0.680 -0.183 0.324
beta4_slope[15] -0.719 0.223 -1.158 -0.717 -0.287
beta4_slope[16] -0.207 0.230 -0.657 -0.212 0.253
sigma_H[1] 0.204 0.055 0.105 0.201 0.321
sigma_H[2] 0.170 0.029 0.117 0.168 0.234
sigma_H[3] 0.195 0.043 0.118 0.193 0.287
sigma_H[4] 0.422 0.076 0.297 0.415 0.596
sigma_H[5] 0.998 0.210 0.622 0.985 1.439
sigma_H[6] 0.385 0.205 0.026 0.378 0.800
sigma_H[7] 0.308 0.063 0.209 0.299 0.461
sigma_H[8] 0.416 0.088 0.281 0.406 0.603
sigma_H[9] 0.524 0.125 0.331 0.506 0.807
sigma_H[10] 0.215 0.042 0.143 0.212 0.305
sigma_H[11] 0.278 0.047 0.201 0.273 0.386
sigma_H[12] 0.429 0.161 0.209 0.400 0.762
sigma_H[13] 0.215 0.038 0.150 0.212 0.298
sigma_H[14] 0.508 0.091 0.351 0.501 0.709
sigma_H[15] 0.245 0.039 0.177 0.241 0.334
sigma_H[16] 0.225 0.043 0.154 0.221 0.324
lambda_H[1] 3.065 3.932 0.155 1.772 12.803
lambda_H[2] 8.121 7.370 0.744 6.053 26.224
lambda_H[3] 6.064 8.344 0.258 3.142 29.699
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 4.001 9.273 0.036 1.154 28.588
lambda_H[6] 7.439 15.526 0.009 0.990 48.661
lambda_H[7] 0.012 0.009 0.002 0.010 0.034
lambda_H[8] 8.376 10.038 0.101 4.965 37.410
lambda_H[9] 0.015 0.010 0.003 0.012 0.040
lambda_H[10] 0.337 1.007 0.037 0.208 1.228
lambda_H[11] 0.260 0.384 0.011 0.126 1.268
lambda_H[12] 4.744 6.239 0.186 2.789 20.997
lambda_H[13] 3.435 3.055 0.218 2.553 11.860
lambda_H[14] 3.338 4.203 0.220 2.049 14.564
lambda_H[15] 0.025 0.032 0.004 0.017 0.102
lambda_H[16] 0.840 1.130 0.048 0.458 3.947
mu_lambda_H[1] 4.336 1.887 1.243 4.162 8.423
mu_lambda_H[2] 3.856 1.944 0.631 3.714 7.985
mu_lambda_H[3] 3.500 1.839 0.749 3.235 7.656
sigma_lambda_H[1] 8.668 4.258 2.056 8.116 18.347
sigma_lambda_H[2] 8.416 4.669 1.074 7.884 18.487
sigma_lambda_H[3] 6.259 3.977 0.985 5.393 15.895
beta_H[1,1] 6.886 1.085 4.298 7.069 8.494
beta_H[2,1] 9.872 0.501 8.779 9.908 10.786
beta_H[3,1] 7.995 0.778 6.219 8.099 9.250
beta_H[4,1] 9.528 7.866 -6.134 9.623 24.461
beta_H[5,1] 0.141 2.232 -4.739 0.305 3.865
beta_H[6,1] 3.246 3.906 -6.650 4.646 7.775
beta_H[7,1] 0.032 5.847 -12.514 0.304 10.479
beta_H[8,1] 1.376 3.834 -2.337 1.265 3.505
beta_H[9,1] 13.044 5.627 1.997 12.949 24.173
beta_H[10,1] 7.029 1.682 3.586 7.082 10.120
beta_H[11,1] 5.032 3.561 -2.780 5.714 9.890
beta_H[12,1] 2.604 1.030 0.683 2.530 4.929
beta_H[13,1] 9.022 0.985 6.844 9.103 10.542
beta_H[14,1] 2.157 1.041 0.056 2.151 4.246
beta_H[15,1] -6.067 3.856 -12.957 -6.351 2.180
beta_H[16,1] 3.428 2.632 -0.710 3.045 9.631
beta_H[1,2] 7.908 0.244 7.388 7.912 8.364
beta_H[2,2] 10.025 0.138 9.754 10.026 10.294
beta_H[3,2] 8.959 0.199 8.568 8.952 9.357
beta_H[4,2] 3.570 1.508 0.624 3.562 6.669
beta_H[5,2] 1.961 0.924 0.130 1.974 3.726
beta_H[6,2] 5.751 1.032 3.348 5.923 7.328
beta_H[7,2] 2.791 1.124 0.811 2.703 5.183
beta_H[8,2] 3.003 1.112 1.292 3.142 4.299
beta_H[9,2] 3.502 1.104 1.421 3.485 5.808
beta_H[10,2] 8.214 0.343 7.520 8.214 8.894
beta_H[11,2] 9.771 0.644 8.845 9.657 11.212
beta_H[12,2] 3.947 0.368 3.241 3.944 4.753
beta_H[13,2] 9.125 0.260 8.666 9.112 9.653
beta_H[14,2] 4.010 0.362 3.311 4.002 4.722
beta_H[15,2] 11.356 0.693 9.895 11.379 12.638
beta_H[16,2] 4.512 0.808 2.976 4.506 6.130
beta_H[1,3] 8.455 0.241 8.016 8.437 8.964
beta_H[2,3] 10.070 0.119 9.833 10.069 10.310
beta_H[3,3] 9.616 0.159 9.301 9.616 9.932
beta_H[4,3] -2.529 0.906 -4.363 -2.517 -0.825
beta_H[5,3] 3.809 0.611 2.533 3.815 4.973
beta_H[6,3] 7.963 1.154 6.366 7.596 10.429
beta_H[7,3] -2.892 0.671 -4.228 -2.872 -1.629
beta_H[8,3] 5.252 0.514 4.664 5.187 6.258
beta_H[9,3] -2.856 0.746 -4.374 -2.848 -1.434
beta_H[10,3] 8.677 0.271 8.147 8.674 9.222
beta_H[11,3] 8.541 0.293 7.918 8.567 9.059
beta_H[12,3] 5.252 0.319 4.494 5.290 5.772
beta_H[13,3] 8.837 0.180 8.469 8.847 9.168
beta_H[14,3] 5.714 0.280 5.103 5.736 6.216
beta_H[15,3] 10.367 0.315 9.754 10.362 10.996
beta_H[16,3] 6.284 0.584 5.000 6.355 7.231
beta_H[1,4] 8.257 0.180 7.863 8.269 8.575
beta_H[2,4] 10.127 0.120 9.877 10.135 10.339
beta_H[3,4] 10.124 0.163 9.781 10.139 10.400
beta_H[4,4] 11.798 0.465 10.861 11.812 12.693
beta_H[5,4] 5.431 0.739 4.258 5.324 7.139
beta_H[6,4] 7.074 0.910 4.970 7.322 8.314
beta_H[7,4] 8.255 0.350 7.571 8.250 8.929
beta_H[8,4] 6.703 0.261 6.225 6.718 7.121
beta_H[9,4] 7.208 0.463 6.317 7.203 8.128
beta_H[10,4] 7.757 0.235 7.339 7.749 8.244
beta_H[11,4] 9.384 0.199 8.992 9.382 9.784
beta_H[12,4] 7.141 0.210 6.734 7.138 7.568
beta_H[13,4] 9.045 0.139 8.765 9.048 9.312
beta_H[14,4] 7.724 0.215 7.318 7.724 8.154
beta_H[15,4] 9.466 0.236 8.989 9.470 9.920
beta_H[16,4] 9.350 0.239 8.910 9.337 9.836
beta_H[1,5] 8.983 0.144 8.686 8.988 9.255
beta_H[2,5] 10.786 0.099 10.602 10.782 10.995
beta_H[3,5] 10.923 0.172 10.613 10.912 11.278
beta_H[4,5] 8.386 0.485 7.470 8.367 9.365
beta_H[5,5] 5.420 0.569 4.132 5.461 6.436
beta_H[6,5] 8.780 0.615 7.880 8.642 10.226
beta_H[7,5] 6.779 0.336 6.140 6.775 7.438
beta_H[8,5] 8.212 0.224 7.858 8.192 8.669
beta_H[9,5] 8.206 0.475 7.262 8.210 9.161
beta_H[10,5] 10.087 0.226 9.635 10.093 10.523
beta_H[11,5] 11.515 0.234 11.074 11.512 11.996
beta_H[12,5] 8.491 0.191 8.124 8.489 8.876
beta_H[13,5] 10.008 0.134 9.756 10.005 10.277
beta_H[14,5] 9.192 0.233 8.751 9.183 9.680
beta_H[15,5] 11.161 0.241 10.669 11.166 11.630
beta_H[16,5] 9.923 0.182 9.558 9.930 10.278
beta_H[1,6] 10.183 0.190 9.836 10.176 10.585
beta_H[2,6] 11.513 0.111 11.300 11.514 11.729
beta_H[3,6] 10.808 0.159 10.471 10.816 11.092
beta_H[4,6] 12.877 0.848 11.115 12.895 14.479
beta_H[5,6] 5.887 0.604 4.764 5.886 7.125
beta_H[6,6] 8.772 0.661 6.994 8.890 9.753
beta_H[7,6] 9.834 0.575 8.648 9.848 10.932
beta_H[8,6] 9.514 0.300 8.972 9.534 9.964
beta_H[9,6] 8.471 0.791 6.990 8.445 10.126
beta_H[10,6] 9.520 0.311 8.862 9.543 10.074
beta_H[11,6] 10.810 0.359 10.036 10.837 11.443
beta_H[12,6] 9.369 0.255 8.892 9.362 9.907
beta_H[13,6] 11.045 0.167 10.752 11.036 11.422
beta_H[14,6] 9.814 0.295 9.203 9.818 10.381
beta_H[15,6] 10.834 0.416 10.048 10.817 11.668
beta_H[16,6] 10.549 0.241 10.043 10.558 11.007
beta_H[1,7] 10.917 0.849 8.993 11.021 12.275
beta_H[2,7] 12.218 0.443 11.332 12.228 13.116
beta_H[3,7] 10.544 0.680 9.005 10.617 11.736
beta_H[4,7] 2.550 4.294 -5.649 2.555 11.359
beta_H[5,7] 6.427 1.814 3.113 6.390 10.410
beta_H[6,7] 9.612 2.387 4.920 9.530 15.758
beta_H[7,7] 10.662 2.909 5.187 10.531 16.484
beta_H[8,7] 10.987 1.116 9.476 10.918 12.763
beta_H[9,7] 4.443 4.085 -4.122 4.539 12.381
beta_H[10,7] 9.827 1.432 7.235 9.747 12.879
beta_H[11,7] 10.983 1.753 7.746 10.862 14.946
beta_H[12,7] 9.987 0.912 7.948 10.069 11.489
beta_H[13,7] 11.657 0.797 9.709 11.754 12.853
beta_H[14,7] 10.384 0.968 8.271 10.445 12.095
beta_H[15,7] 12.026 2.189 7.612 12.083 16.205
beta_H[16,7] 12.270 1.238 10.248 12.122 15.110
beta0_H[1] 8.841 12.980 -16.570 8.968 34.619
beta0_H[2] 10.684 6.188 -2.516 10.789 23.106
beta0_H[3] 9.727 9.951 -10.541 9.971 29.135
beta0_H[4] 4.660 185.075 -371.138 3.582 388.125
beta0_H[5] 4.499 23.382 -40.179 4.536 50.408
beta0_H[6] 8.388 49.681 -88.224 7.865 112.575
beta0_H[7] 7.432 139.250 -264.269 6.115 292.955
beta0_H[8] 6.888 33.249 -15.672 6.354 28.553
beta0_H[9] 7.668 123.627 -238.130 7.235 255.222
beta0_H[10] 8.234 31.967 -53.560 8.272 73.028
beta0_H[11] 11.134 52.418 -91.271 9.794 126.380
beta0_H[12] 6.067 11.408 -18.975 6.431 27.128
beta0_H[13] 9.863 12.102 -9.176 9.673 30.804
beta0_H[14] 6.716 12.418 -17.356 7.013 29.630
beta0_H[15] 8.809 106.872 -211.340 8.672 229.566
beta0_H[16] 7.840 24.516 -42.250 7.581 56.202